Related papers: Optimization schemes for unitary tensor-network ci…

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…

Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix…

The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In…

Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…

We present a pedagogical, hands-on tutorial on \emph{replica tensor-network} techniques for random quantum circuits. At its core, the method recasts circuit-averaged observables acting on multiple copies of the system as the contraction of…

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…

Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis…

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…

Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…

With the advent of quantum and quantum-inspired machine learning, adapting the structure of learning models to match the structure of target datasets has been shown to be crucial for obtaining high performance. Probabilistic models based on…

Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…

The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…

This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…

Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address combinatorial optimization (CO) problems. Using only shallow ansatz circuits, these approaches are deemed…

We present tensor networks for feature extraction and refinement of classifier performance. These networks can be initialised deterministically and have the potential for implementation on near-term intermediate-scale quantum (NISQ)…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…

Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been…

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…